The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Solve like a two-step equation
Use inverse operations to isolate the variable, just like with equations.
An equation says two expressions have the same value. Whatever you do to one side, you must do to the other to keep the balance.
Check your solution by substituting it back into the original equation. If both sides match, your answer is correct.
The one special rule
Solve -2x + 1 < 9.
- 1Subtract 1 from both sides: -2x < 8.
- 2Divide by -2 and flip the sign: x > -4.
Why this matters
Solve like equations - but flip the sign when you multiply or divide by a negative.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Doing different operations to each side of an equation. Whatever you add, subtract, multiply, or divide on one side, do to the other.
Combining unlike terms (like 3x and 4) as if they were the same kind of term.
Key ideas from this lesson
- Solve like a two-step equation
- The one special rule
Video walkthroughs
Multi-Step Inequalities
Solve inequalities and know when to reverse the sign.
Watch on YouTube
Inequalities on a Number Line
Graph two-step inequality solutions on a number line.
Watch on YouTube
Intro to Inequalities
Compare inequality symbols and interpret solution sets.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfSolve: x − 4 > 10.
Step-by-step solution
- 1Add 4 to both sides: x > 14.
Exercise 2
Try it yourselfSolve: 3m + 6 ≤ 21.
Step-by-step solution
- 1Subtract 6: 3m ≤ 15.
- 2Divide by 3: m ≤ 5.
Exercise 3
Try it yourselfSolve: −2x + 8 ≥ 2.
Step-by-step solution
- 1Subtract 8: -2x ≥ -6.
- 2Divide by -2 and flip the sign: x ≤ 3.
Exercise 4
Try it yourselfSolve: 5 − 3y < 14.
Step-by-step solution
- 1Subtract 5: -3y < 9.
- 2Divide by -3 and flip: y > -3.
Exercise 5
Try it yourselfYou need at least $45 for a field trip. You have $18 and earn $9 per chore. How many chores c are needed?
Step-by-step solution
- 1Inequality: 18 + 9c ≥ 45.
- 2Subtract 18: 9c ≥ 27.
- 3Divide by 9: c ≥ 3.
- 4You need at least 3 chores.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Two-Step Inequalities
Question 1 of 4
Solve: 2x + 3 > 11.